Computer aided holography and holographic computer graphics

ABSTRACT

Methods for generating holograms from a computer model of any object employ a combination of numerical and optical means. An illumination model and the light dispersion properties of the objects are specified. The hologram is synthesized from a plurality of smaller hologram elements. Each individual element sustains a field of view of the object. The light rays from the object lying within the field of view and along the lines of sight are sampled by the computer. The sample density should not exceed the resolution limit set by the size of the hologram element. Each light ray is specified by a direction and an amplitude function. The hologram element is obtainable from a Fourier Transform of the sampled rays. In one embodiment, optical means are employed to physically reproduce the sampled light rays using coherent radiation. The reproduced coherent light rays are then interfered with a coherent reference beam to form the hologram element. Alternatively, the interference pattern is calculated directly by the computer and is printed to form the hologram element.

This application is a continuation-in-part of application Ser. No.137,179 filed Dec. 23, 1987, now U.S. Pat. No. 4,778,262.

BACKGROUND OF THE INVENTION

This invention relates generally to the art of computer aided holographyand holographic computer graphics, and more particularly to methodscomprising the use of numerical and optical techniques to generateholograms from a computer model of any object.

Holograms are constructed by recording the interference pattern of acoherent object bearing beam and a coherent reference beam. The image ofthe object is usually reconstructed by directing the same coherentreference beam at the holograms.

Image-plane or focused-image types of holograms are constructed with animage of the object located either very close to or straddling theholographic plate. These holograms have the desirable property that, inreconstruction, the chromatic coherence requirement is relaxed, thusimproving the white-light viewing of the holograms.

In practice, it is often impossible to place the hologram recordingplate very close to an actual object, and impossible for the plate to bestraddled by most objects. Various methods have been used to position animage of the object reconstructed from a hologram at or about theholographic plate. Early focused-image holograms are disclosed by Rosenin his article, "Focused-Image Holography with Extended Sources",published on page 337 of Applied Physics Letters, Vol. 9, No. 9, Nov.1966. The hologram is constructed by placing an image of the object ontothe holographic plate by means of a lens system. This technique issimple, but the maximum field of view is limited by the practicalf-number of the available lenses.

A common technique for making image-plane holograms without field ofview constraints is to employ a two-step holographic method. Aconventional hologram, H1, is first made of an object, and then a. realimage is reconstructed from it. A second holographic plate is positionedcoincident with the real image to make a second, image-plane hologram,H2. Such a two-step technique is disclosed in various forms in U.S. Pat.Nos. 4,339,168, 4,364,627, and 4,411,489. In one form, a hologramconsists of a cylindrical array of lenticular holograms, each made froma different viewpoint of the object. The image is reconstructed in thecenter of the cylinder. A second, focused image hologram may be made bypositioning a hologram recording plate at the center of the cylinder,through a real image reconstructed from it, in a second step.

SUMMARY OF THE INVENTION

It is an important object of the present invention to provide atechnique and system for making a hologram whose object may berepresented on and manipulated by a digital computer, and thus havingthe flexibility of artificial transformation, rendering and animation.

It is another object of the present invention to provide a technique andsystem for making a hologram whose image is reconstructed very close toor straddling the hologram surface without having to use a lens or afirst hologram during construction to image the object onto the hologramsurface.

It is yet another object of the present invention to provide a techniqueand system for making on any given surface relative to the object ahologram whose image is reconstructed without distortion.

These and additional objects of the present invention are accomplished,briefly, by a method wherein the object of the hologram, and the desiredholographic surface, are represented by a model expedient for computermanipulation together with information concerning the illumination ofthe object as well as its reflection and transmission properties. Sincethe object is represented by a computer model, it lends itself simply tothose transformations and animations that are possible with currentcomputer graphics techniques. Furthermore, with a non-real andnon-physical object, the holographic surface may geometrically bedefined in any location close to the object or even straddled by it.

The holographic surface is logically partitioned into a grid within thecomputer, where the contribution of light from the object to each gridelement is envisioned as a bundle of light rays emanating from each partof the object and converging onto each grid element. The amplitude ofeach ray of light arriving at a given grid element is determined by thecomputer by tracing the light ray from the associated part of the objectonto the grid element in accordance with the given illumination model.Thus a "tree" of light rays, each in terms of direction and amplitude,is generated for each grid element. Furthermore, since the illuminationmodel can be manipulated on the computer, the rendering of the objectcan easily be modified. This enables complicated lighting of the objectnot readily practical by physical means.

In order to construct a hologram element at each grid element, theassociated tree of light rays is either physically reproduced usingcoherent radiation and made to interfere with a coherent reference beam,or this interference pattern is calculated in the computer and isprinted point by point, a process which is extremely computationallyintensive. Since the original tree of light rays is duplicated, thefinal reconstructed image will not be distorted. The entire hologram issynthesized by forming, in turn, the hologram element at each gridelement on the holographic surface.

This has only briefly summarized the major aspects of the presentinvention. Other objects, advantages and aspects of the presentinvention will become apparent from the following detailed descriptionwhich should be taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic cross-sectional illustration of a hologram beingmade of a generalized object;

FIG. 2 is a schematic cross-sectional illustration of a modified versionof what is shown in FIG. 1;

FIG. 3A illustrates a partition into grid elements on a generalizedholographic recording surface that can be employed in the illustrationsof FIGS. 1, 2, 4 and 5;

FIG. 3B illustrates a partition into grid elements on a rectangularholographic recording surface that can be employed in the illustrationsof FIGS. 1, 2, 4 and 5;

FIG. 4 is a schematic perspective illustration of a specific embodimentof the present invention;

FIG. 5 shows a modification of the embodiment of FIG. 4;

FIG. 6 illustrates the partition into pixel elements of an element ofthe FIG. 4 and 5 embodiments;

FIG. 7 is a schematic illustration of one possible system that may beemployed to record a transparency formed by any of the embodiments ofFIGS. 1-6;

FIG. 8A is a schematic perceptive illustration of an example opticalsetup for constructing a hologram from transparencies made by techniquesof FIG. 7;

FIG. 8B is a side cross-sectional view of the optical setup of FIG. 8A;

FIG. 8C is an optical setup similar to that of FIG. 8A, butaccomplishing a more exact Fourier Transform relationship between thewindow of pixel elements and the hologram element;

FIG. 9 illustrates another specific arrangement of elemental hologramsformed on a holographic surface;

FIG. 10 shows another specific embodiment of the present invention thatallows construction of a hologram according to FIG. 9;

FIG. 11 illustrates an image point in spherical coordinates, and theresolution limit for an image reconstructed from a hologram element;

FIG. 12 illustrates the system in cylindrical coordinates;

FIG. 13 is an optical setup similar to that of FIG. 8A, butaccomplishing an exact Fourier Transform relationship between the windowof pixels and the hologram element; and

FIG. 14 is the anamorphic version of FIG. 13

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In all the embodiments described herein, an actual object scene isrepresented in a computer data base by a number of computer graphicstechniques. One method suitable for the present invention is the raytracing method of Goldstein et al. in their article entitled "3-D VisualSimulation," published in pp. 25-31 in the Jan. 1971 issue of thejournal Simulation, the disclosure of which is hereby incorporated byreference.

The method uses a conglomeration of elementary geometric building blocksto model an object in a coordinate space. One such technique divides anobject surface into very small areas or three-dimensional objectelements (primitives) whose coordinate locations are stored as part ofthe object data base. In conjunction, an illumination model, whichprovides information concerning the illumination of the object as wellas its reflection and transmission properties, is also specified. Thatis, the degree of dispersion or diffusion, etc. of each primitivesurface element is stated. In this way the amplitude of each light rayas traced by the computer geometrically from a source through reflectionat one par&: of the object to a viewer is determined. A typical exampleof this technique is given by Witted in the article entitled "AnImproved Illumination Model for Shaded Display," published at pp.343-349 of Vol. 23, No. 6, 1980 issue of the journal Communication ofthe Association for Computino Machinerv, the disclosure of which ishereby incorporated by reference.

There are many other techniques of computer modeling which may beincorporated in the methods described herein. Rendering need not berestricted to classical ray tracing methods, but may incorporate surfacetexturing and a variety of other surface rendering techniques. In fact,most techniques of computer graphics modeling may be used.

FIGS. 1 and 2 are illustrations of two different positionings of aholographic surface 50 relative to an object 30, in order to introducethe concepts of the present invention. The holographic surface 50 iswhere the hologram of object 30 is to be constructed. Both the object 30and surface 50 are stored in the computer data base. In general thesurface 50 may take on any shape and may be located anywhere relative tothe object 30. In FIG. 1 a conventional hologram is constructed sincethe surface 50 is located away from the object 30. In FIG. 2 an"image-plane" hologram is constructed since the surface 50 is straddledby the object 30. The use of a computer allows the hologram detectorsurface to be defined to pass through an object, something that cannot,of course, be done with an actual physical detector and object.

Referring to FIG. 3A, the holographic surface 50 is a generalized onethat is geometrically partitioned into a grid with grid elements, suchas elements 52 and 54. In the preferred implementations of the presentinvention, the holographic surface 50 is chosen to be a square orrectangular plate with a partition of square or rectilinear gridelements, as illustrated in FIG. 3B. It is conceptually easier to viewthe hologram as being made up of a large number of contiguoustwo-dimensional hologram elements wherein one element is constructed ata time. It is also a preferred way of performing the calculations andconstruction of the hologram as described hereinafter.

Referring again to FIG. 1, consider two viewers on surface 50 located atthe hologram grid elements 52 and 54, respectively. One light ray whichemanates from a source 10 travels along a path 12 and strikes the object30 at a surface primitive 32. If the surface primitive 32 is diffusive,it will scatter the light ray into a number of secondary rays with acertain amplitude distribution over a given angle. Only the scatteredlight rays along the paths 22 and 24 will be seen by the viewers at 52and 54, respectively. On the other hand, if surface 32 is specular, onlyone secondary ray will arise which in general will not necessarily be inthe line of sight of the viewers at 52 and 54. In the same way anotherlight ray from the source 10 travels along a path 14 and strikes theobject 30 at another surface primitive 34. As before, the viewers 52 and54 will only see the light rays that are scattered into the paths 42 and44, respectively. Thus, it can be seen that the view from each elementon the holographic surface, such as elements 52 and 54, consists oflight rays scattered into it from all surface primitives of the object30.

The description of light interaction with the object need not beconfined to surface scattering. If the object is translucent, forexample, there will be scattering of light within the object. Generally,the view at each grid element consists of the light rays scattered intoit from all parts of the object 30. All of what has been described canbe done in a computer using known computer graphics ray tracingtechniques to implement the embodiments of this invention beingdescribed. Alternatively, these embodiments of the invention can beimplemented by application of other known computer graphics techniques.

Referring to FIG. 2, for the case of an image-plane hologram, theholographic plane 50 is positioned in the computer data base through theobject 30. Light rays emanating from source 10 such as along paths 12and 14 strike the object 30 at surfaces 32 and 34, and scatter into abunch of secondary rays 20 and 40, respectively. The contribution fromthese rays 20 and 40 to the view of a grid element 52 will only comefrom the rays which constructions pass through grid element 52, namely,rays along paths 22 and 42, respectively. Thus, associated with eachgrid element is a view of the object 30, and the view consists of lightrays from all parts of the object 30 which constructions pass throughthat grid element.

The computer is used to sample a representative but discretedistribution of these light rays within each view. Each light ray ischaracterized in the computer by a direction and an amplitude function.Various means may then be employed to physically reproduce these sampledlight rays with coherent radiation having the same directions andamplitudes. In this way, it is as if each grid element of the hologramsurface has a view of the object illuminated by coherent radiation. Ahologram element is then constructed at each grid element when thesereproduced coherent light rays are made to interfere with coherentreference radiation. The entire hologram is finally synthesized byassembling all the constituent hologram elements in the same manner thegrid elements are located adjacent each other on the holographic surface50

Alternatively, one can directly calculate in the computer the actualinterference pattern formed and recorded on the hologram 50 byinterfering each such reflected ray with an appropriate reference beamray. However, because of the extremely large number of points in theobject, each generating ray that impinges on any given small elementalarea of the hologram, and because the amplitude and phase of each suchray must be described, a very large amount of computing power and timeis required to accurately directly construct even a small hologram of avery simple object.

The techniques of a preferred embodiment of the present inventionsystematically select only rays from a limited number of points in theobject for use in constructing each appropriate grid element of thehologram. Furthermore, only the direction and intensity of each ray needbe considered in generating each hologram element. This comes aboutbecause each hologram element is in effect an independent coherentlygenerated hologram. The image generated from each element is onlyincoherently related to that from other elements. This is similar tocomposite (multiplex or lenticular) holography and different fromclassical conventional holography. This independence between elementsresults in resolution limitations in the image. The resolution islimited by the element size, rather than the hologram size as isnormally the case.

It is to be understood that by the term "amplitude" it is generallyreferred to the complex amplitude where the phase is retained. However,in the context of the preferred embodiment, the amplitude refers to theabsolute value of the complex amplitude.

FIG. 11 illustrates the maximum resolution of an image pointreconstructed from a hologram element. Any image point such as 220' mayexpediently be specified in spherical coordinates (R,θ,φ). If theelemental hologram 52 has size in one dimension as "a", then the lateralresolution for the image point 220, at distance R from the hologram isapproximately limited to Rλ/a, where λ is the wavelength of the lightused to reconstruct the hologram. Similarly, in the construction of thehologram element as shown in FIG. 5, the same resolution relationshipexists between the hologram element 52 and any of the pixel elementssuch as 220. The lateral size of the unresolved cell is then seen toincrease with distance from the hologram. Put in another way, thecorresponding angular resolution as denoted by beta in FIG. 11 islimited by the hologram element size, a, to be approximately λ/aradians. This is the minimum angle over which no variations in amplitudeoccur. Thus, the smaller the value of a (and the better the resolutionin the hologram plane) the larger are the unresolved elements in theimage field as well as in the pixel map. There is no need to retainlateral (x and y) resolution to a greater degree than these limitsimpose. The number of rays used to calculate each hologram element isthen reduced.

While the actual image points resulting from the reconstruction of manyadjacent hologram elements may be much smaller than these theoreticallimits just specified, the apparent much better resolution is anartifact, depending on how the elements are placed together and how theyare illuminated. This apparent finer resolution is not based on actualobject data. The actual resolution can, however, be improved byemploying more sophisticated methods in which phase information betweenadjacent hologram elements is calculated. In that case, the hologramelements are no longer incoherent with each other, and greater computingpower and time are required.

The axial (Z direction) resolution is similarly reduced. It isapproximately limited to the lateral resolution R λ/a divided by sin(γ/2) where γ is the total viewing angle retained in the image and inthe entire hologram (see FIG. 11). Thus, for instance, there is no needto specify the object space better than the limit of resolution.

Any computed image which is constructed from data on points spaced muchcloser together than the limits specified above, is inefficientlycreated.

In general, according to the present invention, the amplitude of theselected rays reflected by or transmitted through the object aredetermined by the computer across a surface (not shown in FIGS. 1 and 2)displaced a distance from the object, one such amplitude distributionbeing determined for each of the defined elemental areas of the hologramsurface. The rays from the object that are selected to make up a givenamplitude distribution are those that are on a straight line extendingbetween the hologram grid element and its associated window. The size ofthe windows and their distance from the object define the resultingfield of view of an object image reconstructed from the hologram soconstructed. The resulting amplitude distribution across such a windowis then used to form its respective hologram grid element, eitheroptically or by further computer processing. In either case, however, aphysical, optical hologram results from application of these techniques.An image of the computer defined object is reconstructed from thehologram and viewed by an observer in appropriate light.

Embodiments of the present invention shown in FIGS. 4 and 5 introduce awindow for each hologram element through which the light rays aresampled within each view. Each hologram surface grid element then sees arestricted field of view of the object through the window. FIGS. 4 and 5respectively illustrate the implementing of this technique for the casewith the holographic surface 50 located away from the object 30 (FIG. 4)and the case with surface 50 straddled by the object 50 (FIG. 5). Thewindows 200 and 400 serve to define the field of view for hologram gridelements 52 and 54, respectively. In general there exists one window forthe view of every grid element. A definite pyramid is formed with thewindow at the base and the grid element at the apex. All contribution oflight from the object 30 to a particular grid element must lie withinthe pyramid associated with it. Of course, the shape of the windows canbe something other than rectangular, such as circular, so somethingother than a pyramid will result. Also, the window can be defined to beon a spherical or cylindrical surface. The shape is defined by thedesired field of view and other characteristics of the resultinghologram.

As a particular implementation of computer sampling, a representativedistribution of these light rays from the object 30 is selected by acomputer. Each window is partitioned into a screenful of pixel elements.FIG. 6 illustrates the partitioning of one of the windows, such as 200,in which 220 and 240 are individual pixel elements.

Referring again to FIGS. 4 and 5, consider the pyramid defined by window200 and grid element 52. Each pixel element, such as 220 or 240, maygeometrically be regarded as a unit window through which the gridelement 52 may see a bit of the object 30. For each pixel element,according to a specific example, the computer employs a visible surfacealgorithm to trace from the grid element 52 along a line through thatpixel element and to determine if the line intersects the object 30. Ifan intersection is not found, the computer assigns zero amplitude tothat pixel element and proceeds to the next one. This iterates until anintersection is found. For example, when the algorithm traces throughpixel element 220 along path 22, it will find an intersection with theobject 30 at the surface 32. Execution is then passed onto an amplitudeprocessor where the amplitude of the light ray contributed by thesurface 32 along the traced line is determined in accordance with thespecified illumination model. After assigning the appropriate amplitudevalue to that pixel element 220, the computer returns once again toapply the visible surface algorithm to the next pixel element. Thisiteration proceeds until all pixel elements on the window 200 have beenconsidered. Multiple rays striking a single pixel element are averagedin determining that pixel's amplitude value. This procedure is repeatedso that every grid element's view of the object 30 is encoded as a pixelmap.

A method of performing the calculations for the rays 22 and 42 of FIG.5, and which involves a coordinate transformation may be easilyimplemented in the computer. With this method, for each hologramelement, such as element 52, a spherical coordinate transformation, withelement 52 as its center, is performed on the object field. Thistransformation need be carried out only on the object points within thefield of view spanned by the viewing angle gamma, as shown in FIG. 11.The coordinate of each point in space is specified by (R,θ,φ). Once thetransformation has been performed, a single view is constructed on theobject in much the same way as it is for most standard 3-D graphicssystems. The view so constructed then provides the data on the window200. The view direction is at φ=0, and the view window is ±γ/2. Hiddenline removal and rendering are then carried out by any of the methodscommon to computer graphics.

Similarly, in the case with the anamorphic geometry which is describedlater, cylindrical coordinates (ρ,φ,y) are most expedient. This isillustrated in FIG. 12.

Once the amplitude across each window is determined, the hologram isconstructed one grid element at a time. These hologram elements can becalculated directly by the computer from the amplitude distributionacross their respective windows. Alternatively, FIG. 7 schematicallyillustrates a setup for displaying and making hard copies of each pixelmap in a format suitable for physical regeneration of the rays. Thecomputer 60 is connected to an image display such as a cathode ray, tube(CRT) 62 on which the pixel map is displayed. The display format is inthe form of a screenful of pixel elements identical to the manner eachwindow was partitioned. The brightness of each pixel element is directlyrelated to the amplitude value associated with it. A camera 74 is usedto make a transparency for each window, one for each hologram gridelement.

Each window is usually defined to be the same distance from the hologramsurface as every other, for convenience and in order to provide auniform field of view of the object image from the resulting hologram.However, this does not necessarily have to be the case so long asappropriate corresponding adjustments are made when the final hologramis constructed

The dimensions of the hologram grid elements should be as small aspossible so that they will not be easily visible to the hologram viewer.However, too small a grid element results in a poorly resolved image.Furthermore, the smaller the hologram grid elements, the greater will bethe number of required views of the object scene. If grid elements arenot overlapped, then each grid element represents a single resolved spotin the hologram plane. But in a preferred embodiment previouslydiscussed, if the grid element is very small, then resolution of pointsdistant from the hologram plane suffers, since it is inversely relatedto element size.

FIGS. 8A and 8B illustrate schematically a physical setup for "playingback" the transparencies made in the FIG. 7 setup in coherent radiationto recreate the views as seen by the hologram grid elements so as toform holograms in conjunction with coherent reference radiation. Thetransparencies 68 are played back from a film reel 66 which transportmechanism positions each frame . . . , 200', . . . 400', .. sequentiallyin front of a window 94 on the mask 95. A coherent source 100 passesthrough an optical system 90 before projecting the transparency frame200 through an imaging system 86 onto a holographic recording plate 50through a window 96 on the mask 97. In the absence of scaling, thewindow 96 allows a print identical in size to the grid element 52 ofFIG. 5. The original field of view is illustrated in FIGS. 4 and 5 bythe pyramid in front of grid element 52', and the reproduced field ofview is illustrated in FIGS. 8A and 8B by the pyramid in front ofrecording plate element 52, The imaging system 86 is set up in such away to reproduce the original field of view at recording plate element52, An image 99 of the window transparency 200, is formed before thehologram.

With the view reproduced in coherent light at element 52', a referencebeam is used in conjunction therewith to form a hologram element there.The reference beam is derived from the same coherent source 100, througha beam splitter 91, a series of positioning mirrors 92 and 93, and anoptical system 98, before impinging on recording plate element 52,through the window 96. The recording plate 50, is conveyed by anothertransport mechanism which is synchronized with that of the film reel 66so that as frames . . . 200', . . . , 400', . . . are positioned forplayback, plate 50, is automatically positioned with elements . . . ,52', . . . , 54', . . . behind window 96 for exposure. In this way, byconstructing the hologram element by element, the entire hologram issynthesized.

A preferred embodiment of the present invention is one for which thewindow 200 of FIG. 5 is placed at a very large distance from hologram50. Each window pixel element once again represents a ray direction. Thepixel information in the window may then be regarded as being equivalentto a Fourier Transform of the hologram element.

FIG. 13 illustrates the optical system used to construct the hologram.It is optimized so as to reflect this Fourier relationship. The lens 86performs the Fourier transformation exactly if the film 68 (or an imageof this film) is placed at a distance from a lens 81 equal to its focallength, and furthermore if the hologram 50' is also placed at a distancefrom the lens 86 equal to its focal length.

The setup illustrated in FIG. 8A does not have an exact FourierTransform relationship between, for example, the pixel map 200' and thehologram element 52'. The effect is to introduce some quadratic phaseerrors to the pixel map and also to the hologram element. Nevertheless,for practical purposes, the setup of FIG. 8A is a good approximation,because the hologram element 52' is very small. In FIG. 8A, the errorintroduced to the hologram element can be compensated by having thereference illumination point located in the same plane as the image ofthe grid. Thus, a more exact relationship exists if the reference beamis modified as shown in FIG. 8C. The lens 101 focuses the reference beaminto a point 102 which is ideally at the same distance from the element52' as is the window image 99.

There are alternative arrangements for constructing the compositehologram. For example, if each hologram element contains more than onefocal plane resolvable point, then overlapping hologram elements must beconstructed so as to account for, and capture all the required rays inthe desired viewing angle.

A modification of the embodiment of the present invention enablesgeneration of holograms without vertical parallax. Referring to FIG. 9,the holographic plane 50 is partitioned into vertical strips instead ofgrid elements. Referring to FIG. 10, the view of the object as seen by avertical hologram strip 102 is represented by a wedge instead of apyramid. A window 101 is associated with the strip 102. The ray tracinggoes as before except with the stipulation that the trace through apixel element of each window, such as window 101, and its associatedvertical strip, such as strip 102, must be horizontal; that is, in aline normal to the vertical strip. This added ray selection criteriafurther limits the number of rays that are used to determine theamplitude pattern across the window 101. The imaging device 86 asillustrated in FIGS. 8A and 8B becomes an anamorphic one, such as acylindrical lens. By the same token, the window 96 on mask 97 iscorrespondingly of a shape conforming to the vertical strip.

In the case of the vertical strip, a cylindrical coordinatetransformation with the strip element along the y-axis is performed onthe object field.

An anamorphic system for creating the vertical strip holograms withFourier Transform relationship is shown in FIG. 14. A cylindrical lens130 focuses the vertical lines (i.e., horizontal focus only) in the filmtransparency 200' into the image plane 133, which is further Fouriertransformed in the horizontal direction only, by a cylindrical lens 132.Another Cylindrical lens 131 causes the horizontal lines (vertical focusonly) of transparency 200' to come to focus in the plane of the hologramstrip 102, together with the horizontal Fourier function and thereference beam 134.

Another embodiment of the present invention eliminates the step ofmaking hard copy of the pixel maps. A high resolution electro-opticaldevice is used in place of the transparencies 68 and film reel 66 inFIGS. 8A and 8B. The electro-optical window which is pixel addressableby the computer modulates the transmission of the coherent source 100through each pixel according to the amplitude value associated with it.This allows each hologram to be created as soon as the computed databecomes available for the electro-optic device. A real-time recordingdevice would enable the entire process to be completed quickly. Sometypes of photopolymer are useful for this application because they needvery little post-exposure processing.

Yet another embodiment of the present invention eliminates the step ofmaking hard copy of the pixel maps. Each pixel map or informationequivalent to it is stored in the computer. The corresponding hologramelement is calculated from the pixel map as a Fourier Transform. Theinterference pattern resulting from the Fourier Transform being combinedwith a coherent reference radiation is then calculated and this patternis recorded directly onto the hologram recording plate by such means asan electron beam.

The above description of method and the construction used is merelyillustrative thereof and various changes of the details and the methodand construction may be made within the scope of the appended claims.

It is claimed:
 1. A method of constructing a hologram, comprising the steps of:providing a computer database of information of at least a portion of an object scene and its illumination, defining as computer data and hologram surface with respect to said object scene, dividing the hologram surface into a plurality of elemental areas by means of computer specified boundaries, determining for each of at least some of said plurality of hologram surface areas, by means of a computer, the amplitude and direction of a selected sample of a plurality of rays emanating from an illuminated object that lie only along straight line paths that pass through the given surface area, and constructing a plurality of holograms on a common holographic detector, each of said holograms being formed by redirecting onto the holographic detector the determined amplitude and direction of the sample of rays associated with a corresponding one of the plurality of hologram surface contiguous elemental areas, whereby a completed hologram is formed that is capable of reconstructing an image of said object scene.
 2. A method of constructing a hologram, comprising the steps of:providing a computer database of information of at least a portion of an object scene and its illumination, defining a hologram surface with respect to said object scene, dividing the hologram surface into a plurality of contiguous elemental areas, defining a window at a distance from said hologram for each of at least some of said hologram surface elemental areas, calculating an amplitude variation across each of said windows by collecting rays emanating from the object scene along substantially only straight line paths that pass through both its associated window and hologram surface elemental area, and constructing a hologram in each of at least some of said elemental areas by use of the amplitude variation across its associated window, whereby a completed hologram is formed that is capable of reconstructing an image of said object scene.
 3. A method according to claim 2 wherein the step of defining a hologram surface includes the step of positioning said surface at least partially coincident in space with said object scene, thereby to construct an image plane hologram.
 4. A method according to claim 2 wherein each of said windows is divided into a plurality of pixels whose amplitude is determined by that of at least one of the collected rays.
 5. A method according to claim 2 wherein the step of dividing the hologram surface includes the step of dividing said surface into a plurality of narrow, elongated contiguous areas that are joined along their long sides, thereby to construct a lenticular hologram.
 6. A method according to claim 2 wherein the step of constructing a hologram includes the steps of constructing an object transparency of the resulting amplitude distribution across each window, and using each transparency as an object to optically make an off-axis hologram.
 7. A method of constructing a hologram, comprising the steps of:forming a computer representation of a geometric shape of an object, and its light dispersion characteristics, defining a holographic surface relative to the object, said holographic surface being made up of a plurality of individually defined surface elements, specifying an illumination and dispersion model for the object, for each of at least some of said hologram surface elements, selecting a representative sample of [said]rays from the object with paths lying along a line extending through the surface element, each such ray being specifiable by a direction and a amplitude function, physically reproducing in light said selected sample of rays associated with each said hologram surface element using a first coherent radiation beam such that said directions and amplitude functions are preserved, directing said reproduced light rays and a second radiation beam coherent with said first radiation as a reference beam to said associated surface element to form an interference pattern thereof, and recording and assembling said interference pattern associated with each said surface element at said holographic surface to synthesize said hologram thereof.
 8. A method according to claim 7 wherein the step of defining a hologram surface includes the step of positioning said surface at least partially coincident in space with said object scene, thereby to construct an image plane hologram.
 9. A method according to claim 7 wherein the step of dividing the hologram surface includes the step of dividing said surface into a plurality of narrow, elongated contiguous areas that are joined along their long sides, thereby to construct a lenticular hologram.
 10. The method according to claim 7 wherein the step of selecting a representative sample of rays comprises the steps of:defining a plurality of windows that are individually associated with one of said hologram surface elements, thereby establishing a field of view of the object about said elements, each of said windows additionally having a screenful of pixel elements defined thereon, and selecting only those of said rays from the object that have paths lying along straight lines that pass through said surface element and any one of the pixel elements, thereby to determine the amplitudes of such pixel elements.
 11. The method as in claim 10 wherein the step of physically reproducing a sample cf light rays with coherent radiation comprises the steps of:for each surface element, making a hard copy of the amplitudes of said screenful of pixel elements of each of said windows, said pixels having amplitudes given by said ray amplitude function thereat, and imaging said hard copy with first coherent light to reproduce said sample of light rays onto a surface element at a holographic detector surface such that said ray directions and amplitude functions are preserved.
 12. The method according to claim 11 wherein said surface elements on said holographic surface are in the form of strips such that only those light rays from the object with paths that are perpendicular to said strips and lie along lines therethrough are selected.
 13. The method according to claim 10 wherein said surface elements on said holographic surface are in the form of strips such that only those light rays from the object with paths that are perpendicular to said strips and lie along lines therethrough are selected.
 14. The method as in claim 7 wherein the step of physically reproducing said sample rays with a first coherent radiation beam comprises the steps of:modulating said first coherent radiation beam by passing said beam through a screen, said screen having pixel elements of independent transmission factors, and said transmission factors having been adjusted to reproduce said sample of rays thereof, and imaging said modulated first coherent light beam to reproduce said sample of light rays onto said surface element at said holographic surface such that said directions and amplitude functions are preserved.
 15. The method according to claim 14 wherein said surface elements on said holographic surface are in the form of strips such that only those light rays from the object with paths that are perpendicular to said strips and lie along lines therethrough are selected.
 16. The method according to claim 7 wherein said surface elements on said holographic surface are in the form of strips such that only those light rays from the object with paths that are perpendicular to said strips and lie along lines therethrough are selected.
 17. A method of constructing a hologram, comprising the steps of:providing a computer database of information of at least a portion of an object scene and its illumination, defining as computer data a hologram surface with respect to said object scene, dividing the hologram surface into a plurality of elemental areas by means of computer specified boundaries, determining for each of at least some of said plurality of elemental hologram areas, by means of a computer, the amplitude and direction of a selected sample of a plurality of rays emanating from an illuminated object that lie only along straight line paths that pass through the given elemental hologram area, performing a Fourier Transform on the determined amplitude and direction of the sample of rays for each given elemental hologram area, and constructing a plurality of elemental holograms on a common holographic detector, each of said elemental holograms being formed by recording onto the holographic detector, in combination with a coherent reference radiation, the Fourier Transform of the determined amplitude intensity and direction of the sample of rays associated with each of said elemental holograms, whereby a completed hologram is formed that is capable of reconstructing an image of said object scene.
 18. A method of constructing a hologram as in claim 17, wherein the step of performing the Fourier Transform is done optically by means of a lens system.
 19. A method of constructing a hologram as in claim 17, wherein the step of performing the Fourier Transform is done numerically by means of a computer.
 20. A method of constructing a hologram as in claim 19, wherein the step of forming each of said holograms comprises computing an interference pattern resulting from the combination of the coherent radiation with the Fourier Transform, and recording the interference pattern onto the holographic detector by means of an electromagnetic beam.
 21. A method according to claim 17 wherein the step of defining a hologram surface includes the step of positioning said surface at least partially coincident in space with said object scene, thereby to construct an image plane hologram.
 22. A method of constructing a hologram as in claim 17, wherein "a" denotes a smaller linear dimension of an elemental hologram, λ denotes the wavelength of a reconstructing radiation, and any two adjacent sampled directions are angularly separated by at least λ/a radians.
 23. A method of constructing a hologram as in claim 17, wherein R denotes the distance from an elemental hologram to a point in space, "a" denotes a smaller linear dimension of the elemental hologram, λ denotes the wavelength of a reconstructing radiation, γ denotes the angle defining the maximum span of the sampled directions, and any two points along a direction are spatially separated by at least Rλ/a divided by sin(γ/2).
 24. A method of constructing a hologram as in claim 17, wherein the sampled directions are specified in spherical coordinates.
 25. A method of constructing a hologram as in claim 17, wherein the sampled directions are specified in cylindrical coordinates.
 26. A method of constructing a hologram, comprising the steps of:providing a computer database of information of at least a portion of an object scene and its illumination, defining a hologram surface with respect to said object scene, dividing the hologram surface into a plurality of contiguous elemental areas, defining a window at a distance from said hologram for each of at least some of said hologram elemental areas, calculating an amplitude variation across each of said windows by collecting rays emanating from the object scene along substantially only straight line paths that pass through both its associated window and hologram elemental area, and constructing a hologram in each of at least some of said elemental areas by performing a Fourier Transform on the amplitude variation across the window associated with each elemental area, and recording, in combination with a coherent reference radiation, the Fourier Transform onto the associated elemental hologram area, whereby a completed hologram is formed that is capable of reconstructing an image of said object scene.
 27. A method of constructing a hologram as in claim 26, wherein the step of performing the Fourier Transform is done optically by means of a lens system.
 28. A method of constructing a hologram as in claim 26, wherein the step of performing the Fourier Transform is done numerically by means of a computer.
 29. A method of constructing a hologram as in claim 28, wherein the step of forming each of said holograms comprises computing an interference pattern resulting from the combination of the coherent radiation with the Fourier Transform, and recording the interference pattern onto the holographic detector by means of an electromagnetic beam.
 30. A method according to, claim 26 wherein the step of defining a hologram surface includes the step of positioning said surface at least partially coincident in space with said object scene, thereby to construct an image plane hologram.
 31. A method of constructing a hologram as in claim 26, wherein "a" denotes a smaller linear dimension of an elemental hologram, λ denotes the wavelength of a reconstructing radiation, and any two adjacent sampled directions are angularly separated by at least λ/a radians.
 32. A method of constructing a hologram as in claim 26, wherein R denotes the distance from an elemental hologram to a point in space, "a" denotes a smaller linear dimension of the elemental hologram, λ denotes the wavelength of a reconstructing radiation, γ denotes the angle defining the maximum span of the sampled directions, and any two points along a direction are spatially separated by at least Rλ/a divided by sin(γ/2).
 33. A method of constructing a hologram as in claim 26, wherein the rays are specified by spherical coordinates.
 34. A method of constructing a hologram as in claim 26, wherein the rays are specified by cylindrical coordinates.
 35. A method of constructing a hologram, comprising the steps of:providing a computer database of information of at least a portion of an object scene and its illumination, defining a hologram surface with respect to said object scene, dividing the hologram surface into a plurality of contiguous elemental areas, defining a window at a distance from said hologram for each of at least some of said hologram elemental areas, calculating an amplitude variation across each of said windows by collecting rays emanating from the object scene along substantially only straight line paths that pass through both its associated window and hologram elemental area, and constructing a hologram in each of at least some of said elemental areas by performing an one-dimensional Fourier Transform on the amplitude variation across the window associated with each elemental area, said one-dimensional Fourier Transform being applied along only one axis in the plane of the window, and recording, in combination with a coherent reference radiation, the Fourier Transform onto the associated elemental hologram area, whereby a completed hologram is formed that is capable of reconstructing an image of said object scene.
 36. A method of constructing a hologram as in claim 35, wherein the step of performing the one-dimensional Fourier Transform is done optically by means of a lens system.
 37. A method of constructing a hologram as in claim 35, wherein the step of performing the one-dimensional Fourier Transform is done numerically by means of a computer.
 38. A method of constructing a hologram as in claim 37, wherein the step of forming each of said holograms comprises computing an interference pattern resulting from the combination of the coherent radiation with the one-dimensional Fourier Transform, and recording the interference pattern onto the holographic detector by means of an electromagnetic beam.
 39. A method according to claim 35 wherein the step of defining a hologram surface includes the step of positioning said surface at least partially coincident in space with said object scene, thereby to construct an image plane hologram.
 40. A method of constructing a hologram as in claim 35, wherein "a" denotes a smaller linear dimension of an elemental hologram, λ denotes the wavelength of a reconstructing radiation, and any two adjacent sampled directions are angularly separated by at least λ/a radians.
 41. A method of constructing a hologram as in claim 35, wherein R denotes the distance from an elemental hologram to a point in space, "a" denotes a smaller linear dimension of the elemental hologram, λ denotes the wavelength of a reconstructing radiation, γ denotes the angle defining the maximum span of the sampled directions, and any two points along a direction are spatially separated by at least Rλ/a divided by sin(γ/2).
 42. A method of constructing a hologram as in claim 35, wherein the rays are specified by cylindrical coordinates. 